Existence and uniqueness results for sequential $ \psi $-Hilfer fractional pantograph differential equations with mixed nonlocal boundary conditions

Karim Guida; Lahcen Ibnelazyz; Khalid Hilal; Said Melliani; Karim Guida; Lahcen Ibnelazyz; Khalid Hilal; Said Melliani

doi:10.3934/math.2021477

AIMS Mathematics

2021, Volume 6, Issue 8: 8239-8255. doi: 10.3934/math.2021477

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Existence and uniqueness results for sequential $ \psi $-Hilfer fractional pantograph differential equations with mixed nonlocal boundary conditions

Laboratory of Applied Mathematics and Scientific Computing (LAMSC), Sultan Moulay Slimane University, BP 523 Beni Mellal, Morocco

Received: 15 March 2021 Accepted: 18 May 2021 Published: 26 May 2021
MSC : 26A33, 34A08, 34A12, 34B15

In this paper, we discuss the existence and uniqueness of boundary value problems for sequential $ \psi $-Hilfer fractional pantograph differential equations with mixed nonlocal boundary conditions. The existence results are obtained via the well known Krasnoselskii's fixed point theorem while the uniqueness is demonstrated by using the Banach's contraction mapping principle. Some examples are also given to demonstrate the application of the main results.
- existence,
- uniqueness,
- $ \psi $-Hilfer Fractional derivative,
- pantograph equations,
- fixed point theory
Citation: Karim Guida, Lahcen Ibnelazyz, Khalid Hilal, Said Melliani. Existence and uniqueness results for sequential $ \psi $-Hilfer fractional pantograph differential equations with mixed nonlocal boundary conditions[J]. AIMS Mathematics, 2021, 6(8): 8239-8255. doi: 10.3934/math.2021477

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Abstract

In this paper, we discuss the existence and uniqueness of boundary value problems for sequential $ \psi $-Hilfer fractional pantograph differential equations with mixed nonlocal boundary conditions. The existence results are obtained via the well known Krasnoselskii's fixed point theorem while the uniqueness is demonstrated by using the Banach's contraction mapping principle. Some examples are also given to demonstrate the application of the main results.

References

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